We present MultiMorph, a fast and efficient method for constructing anatomical atlases on the fly. Atlases capture the canonical structure of a collection of images and are essential for quantifying anatomical variability across populations. However, current atlas construction methods often require days to weeks of computation, thereby discouraging rapid experimentation. As a result, many scientific studies rely on suboptimal, precomputed atlases from mismatched populations, negatively impacting downstream analyses. MultiMorph addresses these challenges with a feedforward model that rapidly produces high-quality, populationspecific atlases in a single forward pass for any 3D brain dataset, without any fine-tuning or optimization. MultiMorph is based on a linear group-interaction layer that aggregates and shares features within the group of input images. Further, by leveraging auxiliary synthetic data, MultiMorph generalizes to new imaging modalities and population groups at test-time. Experimentally, MultiMorph outperforms state-of-the-art optimization-based and learningbased atlas construction methods in both small and large population settings, with a 100-fold reduction in time. This makes MultiMorph an accessible framework for biomedical researchers without machine learning expertise, enabling rapid, high-quality atlas generation for diverse studies.